Optimal sap flux sensor allocation for stand transpiration estimates: a non-dimensional analysis

Key message

Measuring between-tree variations in sap flux density rather than azimuthal variations should be prioritized for reliable stand transpiration estimates based on sap flux methods.

Context

Stand transpiration (E) estimated using sap flux methods includes uncertainty induced by azimuthal variations and between-tree variations in sap flux density (F).

Aims

This study examines whether or not measuring F for two or more azimuthal directions to cover azimuthal variations in F leads to more reliable E estimates. This examination was done under the assumption that azimuthal and between-tree variations in F are not systematic and when a limited number of sensors are available.

Methods

We first non-dimensionalized the theoretical framework established by a previous study and developed a general hypothesis. We then validated the hypothesis quantitatively by numerical experiments.

Results

The non-dimensionalized theory allowed us to hypothesize that measuring F for one azimuthal direction would reduce uncertainty in E estimates more effectively than measuring F for two or more azimuthal directions. Results of the numerical experiments were found to support this hypothesis.

Conclusion

When the aforementioned assumptions are satisfied, allocating sensors to measure F for one azimuthal direction to cover between-tree variations in F always leads to more reliable E estimates.

     

Seasonal changes of azimuthal,radial, and tree-to-tree variations in sap flux affect stand transpiration estimates in a <Emphasis Type="Italic">Cryptomeria japonica</Emphasis> forest,central Taiwan

Stand transpiration (E) estimated using the sap flux methods is affected by the azimuthal, radial, and tree-to-tree variations of sap flux. Although several studies have examined the relative importance of the three variations in estimating E, the seasonality of the three variations remains unknown. In the current study, we attempted to clarify whether the relative importance of these three variations could show seasonal changes. Using sap flux data measured in a subtropical cloud forest from August 2010 to July 2011, we calculated the differences resulting from omitting the three variations in estimating E. The effects of the three variations in estimating E showed seasonality. The azimuthal and tree-to-tree variations were more pronounced during winter, whereas the radial variation was more pronounced during summer. However, the effect of tree-to-tree variation was consistently much larger than the other two variations throughout the study period. The tree-to-tree variation is more important in estimating E monthly, seasonally and annually than both the azimuthal and radial variations, although all three variations have shown seasonality. In addition, the sensor allocation for summer would be acceptable for the practical estimation of E if aiming at the long time scale.     

Stand-scale transpiration estimates in a Moso bamboo forest: (I) Applicability of sap flux measurements

The applicability of sap flux (F_d) measurements to bamboo forests has not been studied. This study was undertaken to establish an optimal and effective design for stand-scale transpiration (E) estimates in a Moso bamboo forest. To this aim, we validated F_d measurements in Moso bamboos in a cut bamboo experiment. In addition, we analyzed how sample sizes affect the reliability of E estimates calculated from F_d and conducting culm area (A_{S_b}). In the cut bamboo experiments, we found that F_d measurement using a 10 mm probe was a valid means of determining the water-use behavior of a Moso bamboo, although a specific correction was needed. Furthermore, we calculated E from stand A_{S_b} (A_{S_stand}) and mean stand F_d (J_S). Employing Monte Carlo analysis, we examined potential errors associated with sample size in E, A_{S_stand}, and J_S using an original dataset with A_{S_b} and F_d measured for 40 and 16 individuals, respectively. Consequently, we determined the optimal sample size for both A_{S_stand} and J_S estimates as 11. The optimal sample sizes for J_S were almost the same under different vapor pressure deficit and soil moisture conditions. The optimal sample size for J_S at the study site was less than that of a coniferous plantation in the same region probably owing to small individual-to-individual variations in sap flux in the Moso bamboo forest. Our study concludes that sap flux measurements are an applicable technique for assessing water use in Moso bamboo forests.     

Single-tree water use and water-use efficiencies of selected indigenous and introduced species in the Southern Cape region of South Africa

In South Africa, the development of a plantation tree industry using fast-growing introduced species was accelerated by the limited extent of indigenous forests. However, concerns about the impacts of plantations on the country’s limited water resources has initiated forest hydrology research and subsequent regulation of the industry since 1972. The forestry industry’s continued efforts to sustainably meet fibre and timber demands for the country’s growing economy have prompted questions whether indigenous tree species can provide an additional low water-use form of forestry. Single-tree water use and water-use efficiencies of three indigenous species (Ilex mitis, Ocotea bullata and Podocarpus latifolius) and one introduced species (Pinus radiata) in the Southern Cape region of South Africa were quantified. The heat-pulse velocity method was used to collect hourly sap flow data over a 12-month period. Hourly weather and soil-water data were concurrently recorded and tree growth rates were determined for the year. Biophysical water-use efficiency was calculated as the ratio of utilisable biomass gained per volume of water transpired. Patterns of water use through the year were different for the different species. Pinus radiata had higher transpiration volumes and water-use efficiency levels than the indigenous species. The most transpiring Pinus radiata tree had a transpiration volume that was 4.7 times that of the most transpiring indigenous tree. Indigenous species’ relatively lower water-use efficiencies were more a consequence of slow growth rates and not high water-use rates, which could be attributed to competition for resources in the dense indigenous forest. Potential implications for further hydrological research on the development of water-use-efficient tree production systems are discussed.     

Partition of nocturnal sap flow in Acacia mangium and its implication for estimating the whole-tree transpiration

We analyzed the partition of nocturnal sap flow into refilling of internal water storage and transpiration in Acacia mangium. Sap flow of trees was monitored continuously with Granier’s sensors for estimating the whole-tree transpiration. Possible night transpiration and stomatal conductance at the leaf level in the canopy were measured with a LI-6400 photosynthesis measuring system. For nocturnal leaf transpiration and stomatal conductance were weak, nocturnal sap flow of mature A. mangium trees was mainly associated with water recharge in the trunk. No significant change in night water recharge of the trunk was found at both seasonal and inter-annual scales. Morphological features of trees including diameter at the breast height (DBH), tree height, and canopy size could explain variances of night water recharge. Furthermore, although the contribution of nocturnal sap flow to the total transpiration varied among seasons and DBH classes, the error caused by night water recharge on wholetree transpiration was negligible. __________ Translated from Journal of Plant Ecology (Chinese Version), 2007, 31 (5): 777–786 [译自: 植物生态学报]     

Estimation of whole-stem respiration,incorporating vertical and seasonal variations in stem CO<Subscript>2</Subscript> efflux rate,of <Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis> trees

We examined vertical and seasonal variations in stem respiration rates in a 50-year-old plantation of Japanese cypress, Chamaecyparis obtusa (Sieb. et Zucc.) Endl., in central Japan, and discuss a practical and precise method to scale a point-measured stem CO₂ efflux rate up to whole-stem respiration. For five selected trees, stem CO₂ efflux rates were measured at breast height (1.3 m) and at five or six points above breast height (at approximately 2 m intervals) every 1 or 2 months over two consecutive years. Daily total stem respiration rate (surface area basis) was greater inside the crown than below the crown, especially during the growing season. By incorporating the vertical profile of the respiration rate, annual whole-stem respiration was estimated for each sample tree (R _y). We then compared this estimate (R _y) with another estimate of annual whole-stem respiration (R′_y) obtained using a conventional method; it is assumed that the area-based respiration rate at breast height is constant throughout the stem. The ratio of these two estimates (R′_y/R _y) was usually less than 1, indicating that the assumptions used to calculate R′_y underestimate annual whole-stem respiration. We found that R′_y/R _y was negatively correlated with the ratio of crown length to tree height (crown ratio). These results suggest that annual whole-stem respiration in this C. obtusa plantation is substantially affected by the relative proportion of within-crown stem with higher respiratory activity. Methodologically, our results imply that incorporating the crown ratio into the conventional method would improve the accuracy of annual whole-stem respiration estimates.     

Estimating water use of a black locust plantation by the thermal dissipation probe method in the semiarid region of Loess Plateau, China

Black locust (Robinia pseudoacacia) is a major reforestation species in the semiarid region in the Loess Plateau of China. There has been increasing concern about the sustainability of the plantations because of their possible high water-use. This study was, accordingly, undertaken to quantify the stand-scale water use of a middle-aged black locust plantation in the region. The thermal dissipation probe method was applied to 27 trees to measure sap flux densities in an experimental plot during the growing season of 2008. The monoculture stand has a basal area of 23.3 m² ha^?1 and a maximum plant area index (PAI) of 2.89. Sapwood areas were estimated by use of a regressive relationship with the diameter at breast height (DBH) for scaling up of stand transpiration. The results showed that DBH could be a good predictor of sapwood area of individual trees. The diurnal cycles of average sap flux densities differed among DBH classes. Daily transpiration can be predicted from mean daily daytime vapor pressure deficit (VPD_m) using a fitted exponential saturation model. Model variables were different among seasons, probably owing to different soil water conditions and leaf phenology. By using the derived model for each month, stand canopy transpiration over the growing season was estimated to be 73.8 mm, with an average daily value of 0.41 mm day^?1 and a maximum of 0.89 mm day^?1. The relatively small estimates of stand transpiration might be attributed to low PAI and sap wood area of the middle-aged stand.     

Estimating sap flow from stem heat balances in Quercus robur L. seedlings in relation to light intensity: A comparison of two methods during the establishment phase

? Knowledge of whole tree seedling water fluxes is important in ecological and forestry research, especially under conditions with low transpiration, but no standard method has yet been established that provides reliable in situ measurements.

? The aims were: (1) to assess the performance of two methods for estimating sap-flows in oak seedlings following planting by correlating the data they provided with natural light intensities over a three-week period, and (2) to compare the estimates with transpiration data obtained by weighing pots.

? Estimates of sap flows obtained from data provided by constant power (Dayau-type) heat balance gauges under low light conditions (100–450 μmol m^?2 s^?1) were less variable than estimates from variable power (EMS-type) heat balance gauges. The EMS-type system yielded data with little between-gauge variation, but consistently underestimated transpiration on a daily basis, a systematic error that should be corrected by other methods. The Dayau-type gauges yielded data with substantial variations, and several gauges are probably needed in research to cover these variations. Further, both systems provide rather uncertain estimates of short-time (hour) transpiration rates.

? However, provided that these considerations are taken into account, we conclude that it should be possible to use either system in various research contexts.

     

Growth and ecophysiology of seedlings of Podocarpus falcatus in plantations of exotic species and in a natural montane forest in Ethiopia

The potential role of exotic tree plantations in facilitating successional processes on degraded areas was evaluated in southern Ethiopia by comparing seedling characteristics, transpiration and photo-synthetic performance of Podocarpus falcatus seedlings in Eucalyptus plantation, Pinus plantation, adjacent natural forest and clear-felled plantation site. P. falcatus seedlings exhibited differences in architecture between Eucalyptus and Pinus plantations. They had higher leaf area, shorter internode length and greater number of lateral branches in Eucalyptus plantation. At similar vapor pressure deficit (VPD), P. falcatus transpired much less than E. saligna, especially at higher VPDs. Analysis of fluorescence parameters in the leaves showed no significant differences in the level of dark-adapted and light-adapted fluorescence yield (Fv /Fm and ΔF/Fm, respectively), electron transport rate (ETR) and nonphotochemical quenching (NPQ) among seedlings grown inside plantations and adjacent natural forest, indicating similar photosynthetic performance. Nevertheless, there was evidence of photoinhibition in P. falcatus in the clear-felled site which had low fluorescence yield but high values of NPQ as protection from photoamage. The light response curves of ETR, NPQ and ΔF/F m , showed similar light saturation behavior among the seedlings grown inside plantations and natural forest and suggested a sequence of light-adapted to shade-adapted behavior in Natural forest > Eucalyptus plantation > Pinus plantation. The results show the structural flexibility, better water-use and adaptability of P. falcatus in its use of the understory environment of plantation species.     

Response of canopy stomatal conductance of Acacia mangium forest to environmental driving factors

Granier’s probes were applied to measure the sap flow of 14 sample trees in an Acacia mangium forest on the hilly lands in Heshan City, Guangdong, during the time period of October, 2003. The photosynthetically active radiation (PAR), air relative humidity (RH) and temperature of air (T) above the forest canopy were recorded. The sap flow measurement was used in combination with morphological characteristics of tree and forest structure to calculate the whole-tree transpiration (E), stand transpiration (E _t), and mean canopy stomatal conductance (g _c). Analyses on the relationships between tree morphological characters and whole-tree water use, and on the responses of g _c to PAR and vapor pressure deficit (D) were conducted. The results showed that whole-tree transpiration correlated significantly and positively with tree diameter at breast height (DBH) (p<0.0001), with sapwood area (p<0.0001), and with canopy size (p = 0.0007) logarithmically, but exponentially with tree height (p = 0.014). The analyses on the responses of canopy stomatal conductance showed that the maximum g _c (g _cmax) changed with PAR in a hyperbolic curve (p<0.0001) and with D in a logarithmic one (p<0.0001). The results obtained with sap flow technique indicate its reliability and accuracy of the methods of estimation of whole-tree and stand transpirations and canopy stomatal conductance. __________ Translated from Chinese Journal of Applied Ecology, 2006, 17(7): 1149–1156 [译自: 应用生态学报]     

Nocturnal sap flow characteristics and stem water recharge of Acacia mangium

In this paper, we studied the nocturnal stem water recharge of Acacia mangium. It is helpful to improve the precision of canopy transpiration estimation and canopy stomatal conductance, and to further understand the lag time of canopy transpiration to stem sap flow. In this study, the whole-tree sap flow in an A. mangium forest was measured by using Granier’s thermal dissipation probe for over two years in the hilly land of South China. The environmental factors, including relative humidity (RH), precipitation, vapor pressure deficit (VPD), photosynthetically active radiation (PAR), and air temperature (T _a) were recorded simultaneously. The stem water recharge of A. mangium was analyzed on both daily and monthly scales. Sap flux density was lower at night than during the day. The time range of nighttime sap flux density was longer in the dry season than in the wet season. The water recharging mainly occurred from sunset to midnight. No significant differences were observed among inter-annual nighttime water recharges. Nighttime water recharge had no significant correlation with environmental factors, but was well correlated with the diameter at breast height, tree height, and crown size. In the dry season the contribution of nighttime water recharge to total transpiration had significant correlations with daytime transpiration, total transpiration, VPD, PAR and T _a, while in the wet season it was significantly correlated with daily transpiration and total transpiration. __________ Translated from Chinese Journal of Ecology, 2007, 26(4): 476–482 [译自: 生态学杂志]     

Scaling-up from tree to stand transpiration for a warm-temperate multi-specific broadleaved forest with a wide variation in stem diameter

Previous studies have demonstrated a clear relationship between diameter at breast height (DBH) and tree transpiration (Q _T) in multi-specific broadleaved forests. However, these studies were conducted with a limited range of tree sizes and species, and thus many multi-specific broadleaved forests fall outside these conditions. Therefore, this study examined the relationship between DBH and Q _T in a warm-temperate multi-specific broadleaved forest (n = 12 species) with a wide range of tree sizes (5.0–70.0 cm DBH) using the Granier-type heat dissipation method. The results showed that, although sap flow density varied between individual trees and species, there was a significant relationship between log Q _T and log DBH (r ² = 0.66, P < 0.001) because of the strong dependence of sapwood area on DBH. This study confirmed the applicability of the relationship for the stand transpiration (E _C) estimates even in a multi-specific broadleaved forest with a wide variation in DBH. Our results also revealed that selecting the sample trees in descending order of DBH effectively reduced potential errors in E _C estimates for a specific sample size, as larger trees contribute more to E _C. This information should be useful for future studies investigating the transpiration of multi-specific broadleaved forests, reducing errors during the scaling-up procedure.     

Enhanced transpiration in response to wind effects at the edge of a blue gum (Eucalyptus globulus) plantation

In Australia, tree planting has been widely promoted to alleviate dryland salinity and one proposed planting configuration is that of strategically placed interception belts. We conducted an experiment to determine the effect of tree position in a belt on transpiration rate. We also assessed how much the effect of tree position can be explained by advection and environmental conditions. Daily transpiration rates were determined by the heat pulse velocity technique for four edge and 12 inner trees in a 7-year-old Tasmanian blue gum (Eucalyptus globulus) plantation in South Australia. Various climatic variables were logged automatically at one edge of the plantation. The relationship between daily sap flow and sapwood area was strongly linear for the edge trees (r2 = 0.97), but only moderately correlated for the inner trees (r2 = 0.46), suggesting an edge effect. For all trees, sap flow normalized to sapwood area (Qs) increased with potential evaporation (PE) initially and then became independent as PE increased further. There was a fairly close correlation between transpiration of the edge and inner trees, implying that water availability was partially responsible for the difference between inner and edge trees. However, the ratio of edge tree to inner tree transpiration differed from unity, indicating differences in canopy conductance, which were estimated by an inverse form of the Penman-Monteith equation. When canopy conductances were less than a critical value, there was a strong linear relationship between Qs of the edge and inner trees. When canopy conductances of the edge trees were greater than the critical value, the slope of the linear relationship was steeper, indicating greater transpiration of the edge trees compared with the inner trees. This was interpreted as evidence for enhancement of transpiration of the edge trees by advection of wind energy.     

Variation in the radial patterns of sap flux density in pubescent oak (Quercus pubescens) and its implications for tree and stand transpiration measurements

Radial variation in sap flux density across the sapwood was assessed by the heat field deformation method in several trees of Quercus pubescens Wild., a ring-porous species. Sapwood depths were delimited by identifying the point of zero flow in radial patterns of sap flow, yielding tree sapwood areas that were 1.5-2 times larger than assumed based on visual examinations of wood cores. The patterns of sap flow varied both among trees and diurnally. Rates of sap flow were higher close to the cambium, although there was a significant contribution from the inner sapwood, which was greater (up to 60% of total flow) during the early morning and late in the day. Accordingly, the normalized difference between outer and inner sapwood flow was stable during the middle of the day, but showed a general decline in the afternoon. The distribution of sap flux density across the sapwood allowed us to derive correction coefficients for single-point heat dissipation sap flow measurements. We used daytime-averaged coefficients that depended on the particular shape of the radial profile and ranged between 0.45 and 1.28. Stand transpiration calculated using the new method of estimating sapwood areas and the radial correction coefficients was similar to (Year 2003), or about 25% higher than (Year 2004), previous uncorrected values, and was 20-30% of reference evapotranspiration. We demonstrated how inaccuracies in determining sapwood depths and mean sap flux density across the sapwood of ring-porous species could affect tree and stand transpiration estimates.     

Evaluation of sap flow density of <Emphasis Type="Italic">Acacia melanoxylon</Emphasis> R. Br. (blackwood) trees in overstocked stands in north-western Iberian Peninsula

Sap flow density and meteorological variables were monitored in a very dense Acacia melanoxylon stand (about 9,000 trees/ha) in north-western Iberian Peninsula during the growing season of 2006 (from 8 June to 24 August). Evidences of an increment of stomatal control on transpiration were observed during the study period, probably as a consequence of higher evaporative demand of the atmosphere. However, high sap flow density values observed for the whole study period (from 1.14 to 52.73 dm³ dm⁻² day⁻¹) were similar than those found for other fast-growing species. Mean transpiration for the whole study period was 2.21 mm day⁻¹, with a maximum value of 3.17 mm day⁻¹ and a minimum of 1.23 mm day⁻¹. Mean sap flow density values were correlated with crown length and crown ratio, relationships being fairly weak with other dendrometric parameters such as tree diameter or height. Mean transpiration values were correlated with main dendrometric parameters (diameter at breast height, total height, crown length, sapwood area and leaf biomass). It was found that the degree of competition per tree could be used as a good index for sap flow density. Taking into account the high tree density of the stand and the sap flow density values, water consumptions of A. melanoxylon can be very high, playing a relevant role in the hydrological balances of the watersheds where it grows.     

Early growth and photosynthetic responses to light in seedlings of three tropical species differing in successional strategies

Containerized seedlings of three commercially important tropical species were grown under four different light treatments [i.e., 100 (open site), 45, 22 and 10% sunlight] for 130 days. Light-saturated photosynthesis (A _max) and light saturation estimates (LSE) reflected the species successional status with Terminalia superba Engl. and Diels, the pioneer species showing largest mean A _max and LSE at 100% sunlight, whereas at 10% sunlight, it showed the lowest A _max and LSE. At 22% sunlight, Cedrela odorata L., an intermediate successional species had greater A _max and LSE than Mansonia altissima A. Chev., a non-pioneer light demander and T. superba. T. superba had the lowest relative growth rate (RGR) at 10% sunlight and greatest net assimilation rate (NAR) at 100% sunlight; although a higher RGR at this light level was not seen for this species. Strong and positive linear mean A _max–mean NAR relationship of C. odorata and T. superba indicated that differences in leaf photosynthetic rates of the two species were reflected in their NAR, which increased with increasing light. At final harvest, superior biomass production was found at 45% sunlight for all the species. Seedling responses in specific leaf area, leaf area ratio, leaf mass ratio and root mass ratio were typically those found along a light gradient. At the 100% sunlight, intrinsic water-use efficiency (WUE), F _v/F _m and final root system of the plants was generally superior in T. superba but at 10% sunlight, WUE was inferior in T. superba when compared to C. odorata and M. altissima, reflecting the respective species’ short-term acclimation to high or low light. Results of this study may have practical use in screening tropical tree species for use in plantation forestry.     

Sap flow of irrigated <Emphasis Type="Italic">Populus alba</Emphasis> var. <Emphasis Type="Italic">pyramidalis</Emphasis> and its relationship with environmental factors and leaf area index in an arid region of Northwest China

Populus alba L. var. pyramidalis Bge. (Populus) is a main tree of the farmland shelter-belt system in the arid region of Northwest China. However, soil moisture cannot satisfy the water requirements of normal Populus growth under local natural conditions, thus studying the transpiration characteristics of irrigated Populus and its relationship with the environmental factors and growth parameters is very important to the growth of the trees in this region. In this study, the sap flow of two irrigated Populus trees was measured during May to September from 2005 to 2008 using the heat-pulse technique. The results show that the maximum and minimum daily sap fluxes in Populus were 15.7–24.0 and 3.0–4.0 L day⁻¹, respectively. And the sum of sap fluxes from June to August accounted for approximately 63–69% of the total sap flux during May to September (almost the whole growing season). The order of the meteorological factors affecting the daily sap flux of Populus was: vapor pressure deficit > solar radiation > mean air temperature > wind speed. Furthermore, a highly linear relationship between the ratio of daily sap flux to the reference evapotranspiration (SF/ET₀) and the amount of soil water in the 0–2.0 m layer was found, indicating that the amount of soil water at this layer was quite important to the growth of Populus in this region. Especially, the amount of soil water in the 0.5–1.0 m soil layer contributed to most of the plant transpiration as the highest coefficient of determination at this layer. Based on the environmental factors and leaf area index influencing sap flux, an empirical transpiration model was constructed to estimate daily transpiration.     

Estimating stand transpiration in a Eucalyptus populnea woodland with the heat pulse method: measurement errors and sampling strategies

Sap flow measurement techniques, such as the heat pulse (compensation) method, are practical means for estimating the water use of individual trees and are often the only reasonable alternative for measuring forest and woodland transpiration in complex heterogeneous terrain. The need to scale estimates of water use from a sample of individual stems to a stand (population) of known area may be satisfied by applying scalars of flux based on tree size or domain. We estimated the aggregate errors in applying the heat pulse technique to the estimation of stand transpiration in a poplar box (Eucalyptus populnea F.J. Muell.) woodland in southeastern Queensland, Australia, by a combination of precision analyses, experimental validation and Monte Carlo simulations of sampling errors. Errors in sap flux density measurements were approximately 13%. The potential error in the flux estimates for individual stems with stratified sampling of sap flux density with depth and bole quadrant based on four sensors was an additional 25%. Conducting wood area, diameter at 1.3 m, leaf area and domain based on Ecological Field Theory all proved excellent scalars of flux at the stand level. With a sample size of six trees stratified by diameter, coefficients of variation in scaling to the stand level were approximately 5% for any of these scalars. The greatest potential source of error in estimating stand transpiration by the heat pulse method was in the measurement of the fluxes of individual stems; scaling these measurements to a homogeneous stand of trees involved less uncertainty.     

木麻黄南北方位边材液流季节动态及其对蒸腾耗水测算的影响

利用TDP径流计对福建沿海木麻黄南北方位的边材液流动态进行长期监测，并同步检测空气温湿度、太阳辐射等环境因子，分析南北方位液流速率的相互关系、对蒸腾耗水量测算的影响以及与环境因子的关系。结果显示，木麻黄南北2个方位测得的液流速率存在显著差异和线性相关。木麻黄生长季（5～10月）内单株蒸腾耗水量与日总太阳辐射和昼间平均空气水汽压亏缺的指数饱和曲线拟合效果较好。采用单方位树干液流速率测算的整株蒸腾耗水量与2个方位的测算值相差18．19％。     

Allometric model of the Reineke equation for Japanese cypress (<Emphasis Type="Italic">Chamaecyparis obtusa</Emphasis>) and red pine (<Emphasis Type="Italic">Pinus densiflora</Emphasis>) stands

An allometric model that explains the mechanism of the difference in the slope of the Reineke equation (A) among species was proposed based on the allometric relationships of mean tree height (H) to quadratic mean diameter D (H ∝ D ^θ ) and stand density N (H ∝ N ^δ ), i.e., A = θ/δ. The proposed model was fitted to Japanese cypress (Chamaecyparis obtusa Endl.) and red pine (Pinus densiflora) stands. The allometric exponents θ and δ were, respectively, 0.8995 and −0.5000 for cypress and 0.8612 and −0.6619 for pine. The difference between cypress and pine was significant for δ but not for θ. Inserting the exponents into the model resulted in predicted slopes of −1.7991 for cypress and −1.3011 for pine. The difference in the slope of the Reineke equation between the two species was produced by characteristics related to the tree crown, rather than characteristics related to stem slenderness. The proposed model enables us to estimate the slope of the Reineke equation from commonly measured stand attributes, such as mean tree height and quadratic mean diameter. Therefore, the proposed model is expected to be practical and convenient for estimating the slope of the Reineke equation and for explaining the mechanism of its variation among species. The model should be also accepted as a generalized model of the stand density versus quadratic mean diameter relationship, whereas the original Reineke equation should be seen as a specific case of this model.